Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning

We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general approach under modest assumptions. More specifically, the convexity criterion might not be satisfied by the objective function. Unlike descent line-search algorithms, it does not require an initial step-size to be determined by a previously determined Lipschitz constant. The process's primary characteristic is its gradual step-size reduction …

applications assumptions class convergence criterion cs.lg general gradient line line-search math.oc multi-task learning optimization programming prove search set vector